39 
The Theory of Geotropic Response 
especially in the diversity of reaction of the stem and the root. 
Professor Small has therefore shown great courage in attacking the 
problem and great ingenuity in working out his theory. Our 
knowledge of the colloidal and electrical conditions of the living 
cell is unfortunately so slight that any theory of this kind must be 
highly speculative, but in considering the theory as a working 
hypothesis a number of serious difficulties appear to arise, some of 
which are here put forward. 
(i) One difficulty—and it is naturally a fundamental one—is as 
to the actual occurrence of the " creaming” effect. As is well known, 
there is no obvious settling of colloidal solutions; gold solutions 
made by Faraday more than sixty years ago are still to be seen at 
the Royal Institution. Yet, on the other hand, far smaller particles, 
for example, gaseous molecules, do settle to some extent as is clearly 
shown by the decrease in air pressure as we rise above sea-level. 
The explanation of this apparent discrepancy is that all particles 
settle to some degree, whether they are gaseous, molecules, ultra- 
microscopic particles, or microscopic particles; but the degree to 
which they settle (i.e. the alteration of concentration with height) 
depends on the volume of the particles and their relative density. 
The atmosphere follows what is called the exponential "rarefaction 
law”; if we go up six kilometres the density (i.e. concentration of 
molecules) falls to one-half, if we go up another six kilometres it 
falls to one-quarter, and so on. Einstein in 1905, and independently 
Perrin in 1908, showed that if the Brownian movement of particles 
is due to molecular bombardment the distribution with height of 
such particles must follow the same law. The amount of settling or 
rising for any given height—whether the particles are gaseous 
molecules or colloidal particles—will depend on the volume of the 
molecules or particles and their density. Perrin 1 was able to demon¬ 
strate by examination of carefully prepared colloidal solutions of 
gamboge and mastic that the particles did obey the "rarefaction 
law,” for at each equal step upwards the concentration of particles 
decreased in geometrical progression. Perrin, in one of his experi¬ 
ments, found that for gamboge particles of radius 0*21 fi the con¬ 
centration was halved for each rise in height of 30 /jl. 
From data such as these of Perrin’s we can obtain some 
idea of the degree of settling or "creaming” which would result 
from the action of gravity on the colloidal particles of the proto¬ 
plasm. Perrin worked with microscopic particles; the protoplasmic 
1 J. Perrin, Brownian Movement and Molecular Reality. (English transla¬ 
tion), London, 1910; also Atoms (English translation), London, 1916. 
